MINNEAPOLIS—Abdi Mohamed strode into a coffee shop on a recent morning and took a lap around the place, shaking hands with about a dozen men as they paused their lively discussions of the news of the day to give him a warm greeting.

“This is our place,” he said of the Starbucks in the Seward neighborhood, where thousands of Somalis live. “This might be the loudest Starbucks in the United States.”